Sequence Calculator With Answers

Common Sequence Formulas:

\[ \text{Arithmetic: } a_n = a_1 + (n-1)d \] \[ \text{Geometric: } a_n = a_1 \times r^{(n-1)} \] \[ \text{Fibonacci: } F_n = F_{n-1} + F_{n-2} \]

Term Value (aₙ):

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1. What is a Sequence Calculator?

A sequence calculator computes the nth term of mathematical sequences. It can handle arithmetic, geometric, and Fibonacci sequences, providing both the answer and the formula used.

2. How Does the Calculator Work?

The calculator uses different formulas based on sequence type:

\[ \text{Arithmetic: } a_n = a_1 + (n-1)d \] \[ \text{Geometric: } a_n = a_1 \times r^{(n-1)} \] \[ \text{Fibonacci: } F_n = F_{n-1} + F_{n-2} \]

Where:

\( a_n \) — nth term of the sequence
\( a_1 \) — first term
\( d \) — common difference (arithmetic)
\( r \) — common ratio (geometric)
\( n \) — term number

3. Types of Sequences

Arithmetic: Each term increases by a constant difference (e.g., 2, 5, 8, 11... with d=3).

Geometric: Each term is multiplied by a constant ratio (e.g., 3, 6, 12, 24... with r=2).

Fibonacci: Each term is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5...).

4. Using the Calculator

Steps: Select sequence type, enter first term, common difference/ratio (if applicable), and term number. The calculator will display the nth term and formula used.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arithmetic and geometric sequences?
A: Arithmetic adds a constant difference, while geometric multiplies by a constant ratio.

Q2: Why does Fibonacci sequence start with 0 and 1?
A: By definition, F₀=0 and F₁=1. This is the standard modern convention.

Q3: Can I calculate negative term numbers?
A: The calculator only accepts positive integers for term numbers.

Q4: What about other sequence types?
A: This calculator focuses on the three most common sequence types.

Q5: How accurate are the calculations?
A: Calculations are precise to floating-point arithmetic limits.